Abstract:

The effect of a time harmonic electric source ring placed
axially symmetric between the walls of a double conical structure of
finite slant height is investigated. The bases of the conical structures
are spherical caps of radii equal to the slant height.
The Green's function for ideally conducting walls is obtained
using the normalized eigenfunction expansion theorem. The magnetic
and electric components of the induced electromagnetic field are obtained
in the form of a single infinite series.
The solution is investigated for several special cases. The
special cases include the finite single cone, semi-infinite single cone,
semi-infinite double cone, and biconical antenna.
The heat conduction problem for the identical geometry is
solved also. The solution is obtained by employing the theory of
Laplace transformations on the Green's function for the electric source ring. Two cases, finite and semi-infinite slant heights, present
two forms of solutions. Finite slant height yields a double infinite
series and semi-infinite slant height a single infinite series.